We address the issue of learning multi-layered perceptrons (MLPs) in a
discriminative, inductive, multiclass, parametric, and semi-supervised
fashion. We introduce a novel objective function that, when optimized,
simultaneously encourages 1) accuracy on the labeled points, 2)
respect for an underlying graph-represented manifold on all points, 3)
smoothness via an entropic regularizer of the classifier outputs, and
4) simplicity via an l2 regularizer. Our approach provides a simple,
elegant, and computationally efficient way to bring the benefits of
semi-supervised learning (and what is typically an enormous amount of
unlabeled training data) to MLPs, which are one of the most widely
used pattern classifiers in practice. Our objective has the property
that efficient learning is possible using stochastic gradient descent
even on large datasets. Results demonstrate significant improvements
compared both to a baseline supervised MLP, and also to a previous
non-parametric manifold-regularized reproducing kernel Hilbert
space classifier.